Problem: Igor the analyst has adopted n little bunnies. As we all know, bunnies love carrots. Thus, Igor has bought a carrot to be shared between his bunnies. Igor wants to treat all the bunnies equally, and thus he wants to cut the carrot into n pieces of equal area. 

Formally, the carrot can be viewed as an isosceles triangle with base length equal to 1 and height equal to h. Igor wants to make n - 1 cuts parallel to the base to cut the carrot into n pieces. He wants to make sure that all n pieces have the same area. Can you help Igor determine where to cut the carrot so that each piece have equal area?

<image> Illustration to the first example.

Input

The first and only line of input contains two space-separated integers, n and h (2 ≤ n ≤ 1000, 1 ≤ h ≤ 105).

Output

The output should contain n - 1 real numbers x1, x2, ..., xn - 1. The number xi denotes that the i-th cut must be made xi units away from the apex of the carrot. In addition, 0 < x1 < x2 < ... < xn - 1 < h must hold. 

Your output will be considered correct if absolute or relative error of every number in your output doesn't exceed 10 - 6.

Formally, let your answer be a, and the jury's answer be b. Your answer is considered correct if <image>.

Examples

Input

3 2


Output

1.154700538379 1.632993161855


Input

2 100000


Output

70710.678118654752

Note

Definition of isosceles triangle: <https://en.wikipedia.org/wiki/Isosceles_triangle>.

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
int main() {
  double n, h;
  int i;
  cin >> n >> h;
  double temp1 = sqrt(2.0 / 3.0);
  double temp2 = sqrt(1.0 / 2.0);
  if (n == 2) {
    double temp = h * temp2;
    printf("%.12lf\n", temp);
    return 0;
  }
  vector<double> ans;
  ans.push_back(h * sqrt((double)(n - 1) / (double)(n)));
  for (i = n - 2; i >= 1; i--) {
    ans.push_back(ans[n - 2 - i] * sqrt((double)(i) / (double)(i + 1)));
  }
  reverse(ans.begin(), ans.end());
  int len = ans.size();
  for (i = 0; i < n - 1; i++) printf("%.12lf ", ans[i]);
  cout << endl;
  return 0;
}